Solving N-Queen Problem using Las Vegas Algorithm with State Pruning

TL;DR

This paper presents a hybrid Las Vegas algorithm with state pruning for the N-Queen problem, significantly improving solution speed and efficiency over traditional methods, especially for large N, by reducing search space and computational cost.

Contribution

It introduces a novel hybrid algorithm combining Las Vegas stochastic approach with iterative pruning to enhance performance in solving large N-Queen instances.

Findings

The hybrid algorithm outperforms backtracking in speed for large N.

It reduces search space through dynamic pruning during random placement.

The method offers a good balance between solution quality and computational efficiency.

Abstract

The N-Queens problem, placing all N queens in a N x N chessboard where none attack the other, is a classic problem for constraint satisfaction algorithms. While complete methods like backtracking guarantee a solution, their exponential time complexity makes them impractical for large-scale instances thus, stochastic approaches, such as Las Vegas algorithm, are preferred. While it offers faster approximate solutions, it suffers from significant performance variance due to random placement of queens on the board. This research introduces a hybrid algorithm built on top of the standard Las Vegas framework through iterative pruning, dynamically eliminating invalid placements during the random assignment phase, thus this method effectively reduces the search space. The analysis results that traditional backtracking scales poorly with increasing N. In contrast, the proposed technique consistently generates valid solutions more rapidly, establishing it as a superior alternative to use where a single, timely solution is preferred over completeness. Although large N causes some performance variability, the algorithm demonstrates a highly effective trade-off between computational cost and solution fidelity, making it particularly suited for resource-constrained computing environments.